含阻尼项的SRLW方程的一个去耦合线性化差分格式

A decoupled linearized difference scheme for the SRLW equation with damping term

摘要:

本文对带有阻尼项的耗散SRLW方程的初边值问题进行了数值方法研究，提出了一个具有二阶理论精度的三层非耦合线性化差分格式.该格式解除了原方程中函数之间的耦合关系，大大提高了数值求解效率.此外，本文综合运用数学归纳法和离散泛函分析方法证明了格式的收敛性和稳定性.数值实验表明该方法是可靠的.

Abstract:

In this paper, a numerical method for the initial-boundary value problem of the dissipative SRLW equation with damping term is considered. A three-level uncoupled linearized difference scheme with second order accuracy is introduced. Though the maximum modulus estimation of the difference solution fails to be obtained, we still prove the convergence and stability of the numerical solution directly by the inductive method and discrete functional analysis. Finally, the efficiency of the method is demonstrated by numerical examples.